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Register a new userFirst order dissipative hydrodynamics and viscous corrections to the entropy four-current from an effective covariant kinetic theory
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The first order hydrodynamic evolution equations for the shear stress tensor, the bulk viscous pressure and the charge current have been studied for a system of quarks and gluons, with a non-vanishing quark chemical potential and finite quark mass. The first order transport coefficients have been obtained by solving an effective Boltzmann equation for the grand-canonical ensemble of quasiquarks and quasigluons. We adopted temperature dependent effective fugacity for the quasiparticles to encode the hot QCD medium effects. The non-trivial energy dispersion of the quasiparticles induces mean field contributions to the transport coefficients whose origin could be directly related to the realization of conservation laws from the effective kinetic theory. Both the QCD equation of state and chemical potential are seen to have a significant impact on the quark-gluon plasma evolution. The shear and bulk viscous corrections to the entropy-four current have been investigated in the framework of the effective kinetic theory. The effect of viscous corrections to the entropy density have been quantified in the case of one dimensional boost-invariant expansion of the system. Further, the first order viscous corrections to the time evolution of temperature along with the description of pressure anisotropy and Reynolds number of the system have been explored for the longitudinal boost-invariant expansion.volution of temperature along with the description of pressure anisotropy of the system have also been explored.
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The second-order hydrodynamic equations for evolution of shear and bulk viscous pressure have been derived within the framework of covariant kinetic theory based on the effective fugacity quasiparticle model. The temperature-dependent fugacity parameter in the equilibrium distribution function leads to a mean field term in the Boltzmann equation which affects the interactions in the hot QCD matter. The viscous corrections to distribution function, up to second-order in gradient expansion, have been obtained by employing a Chapman-Enskog like iterative solution of the effective Boltzmann equation within the relaxation time approximation. The effect of mean field contributions to transport coefficients as well as entropy current has been studied up to second-order in gradients. In contrast to the previous calculations, we find non-vanishing entropy flux at second order. The effective description of relativistic second-order viscous hydrodynamics, for a system of interacting quarks and gluons, has been quantitatively analyzed in the case of the $1+1-$dimensional boost invariant longitudinal expansion. We study the proper time evolution of temperature, pressure anisotropy, and viscous corrections to entropy density for this simplified expansion. The second order evolution of quark-gluon plasma is seen to be affected significantly with the inclusion of mean field contributions and the realistic equation of state.
We find that the recently developed kinetic theories with spin for massive and massless fermions are smoothly connected. By introducing a reference-frame vector, we decompose the dipole-moment tensor into electric and magnetic dipole moments. We show that the axial-vector component of the Wigner function contains a contribution from the transverse magnetic dipole moment which accounts for the transverse spin degree of freedom (DOF) and vanishes smoothly in the massless limit. As a result, the kinetic equations, describing four DOF for massive fermions, becomes smoothly the chiral kinetic equations describing two DOF in the massless limit. We also confirm the small-mass behavior of the Wigner function by explicit calculation using a Gaussian wave packet.
We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the $O(1/mu)$ expansion, but in agreement with the equation derived in on-shell effective field theory upon identification of cutoff. By using reparametrization transformation properties of the effective theory, we show that the difference in kinetic equations from two approaches are in fact expected. It is simply due to different choices of degree of freedom by effective theory and field theory. We also show that they give equivalent description of the dynamics of chiral fermions.
We extended our formulation of causal dissipative hydrodynamics [T. Koide textit{et al.}, Phys. Rev. textbf{C75}, 034909 (2007)] to be applicable to the ultra-relativistic regime by considering the extensiveness of irreversible currents. The new equation has a non-linear term which suppresses the effect of viscosity. We found that such a term is necessary to guarantee the positive definiteness of the inertia term and stabilize numerical calculations in ultra-relativistic initial conditions. Because of the suppression of the viscosity, the behavior of the fluid is more close to that of the ideal fluid. Our result is essentially same as that from the extended irreversible thermodynamics, but is different from the Israel-Stewart theory. A possible origin of the difference is discussed.
We derive the equations of second order dissipative fluid dynamics from the relativistic Boltzmann equation following the method of W. Israel and J. M. Stewart. We present a frame independent calculation of all first- and second-order terms and their coefficients using a linearised collision integral. Therefore, we restore all terms that were previously neglected in the original papers of W. Israel and J. M. Stewart.
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